## Abstract

Private assets, such as private equity, venture capital, and real estate, have long been a thorn in the side of asset allocators and chief investment officers. Their lack of liquidity makes it hard to analyze their return stream and to construct a performance attribution. The illiquid nature of these assets often leads to misspecification and estimation of the systematic risk embedded in their returns and the true amount of alpha generated by these managers.

**TOPICS:** Real assets/alternative investments/private equity, manager selection, performance measurement

Private assets, such as private equity, venture capital, and real estate, have long been a thorn in the side of asset allocators and chief investment officers. Their lack of liquidity makes it hard to analyze their return stream and construct a performance attribution. The illiquid nature of these assets often leads to misspecification and incorrect estimation of the systematic risk embedded in their returns and the true amount of alpha generated by these managers.

Illiquid assets trade infrequently, and their lack of movement with the liquid financial markets increases both their liquidity risk and the risk that their infrequent trading will not be sufficiently taken into account in the performance attribution process. As a result, this can lead to consultants, allocators, and chief investment officers recommending a greater allocation to private assets than may be warranted by their underlying economics.

A number of articles have reviewed the liquidity issue. Lo, Petrov, and Wierzbicki [2003] considered liquidity to be a constraint in a mean-variance portfolio construction. Ang and Bollen [2010] reviewed the impact of lock ups as a liquidity option. Kinlaw, Kritzman, and Turkington [2013] viewed liquidity as an overlay to the portfolio construction process. Siegel [2008] demonstrated how capital calls associated with illiquid assets can operate like an off-balance-sheet liability. Most recently, Lindsey and Weisman [2016] presented a method to value the cost of liquidity as an up-and-in barrier option when the credibility threshold of a private asset manager is breached.

In this article, we focus on measuring the full amount of systematic risk embedded in the returns to private asset classes. More specifically, we demonstrate that a significant amount of lagged beta is embedded in the returns to private assets. In addition, we construct a liquidity premium index that we use to determine how much of the return to illiquid assets is from the liquidity premium and how much is from manager skill. We find that when we account for the true amount of systematic (beta) risk and an accurate measure of the liquidity premium, the resulting alpha produced by private asset managers declines significantly.

## A REVIEW OF ILLIQUID ASSET CLASSES

Malkiel [2012] demonstrated that efficient markets make it impossible to consistently use today’s asset price to predict what will happen tomorrow, nor can yesterday’s asset price predict the return with today’s asset price. Public asset prices follow a random walk, in which the path of the asset price cannot be predicted based on looking back in time. Because the acquisition of information in the public markets is essentially costless and new information becomes embedded in public asset prices immediately, the only way to extract value in public markets is through superior fundamental analysis that leads to positive outperformance, or alpha.

Such an assumption, however, may not be true for illiquid asset classes, such as private equity, venture capital, and real estate. For private assets, information is not freely available, and the acquisition of information is costly, thus making the private asset market less efficient than the public securities markets. Consequently, private equity, venture capital, and real estate valuations are less likely to follow a random walk.

The informational asymmetries found in private assets occur for several reasons and have implications for performance measurement. First, Jian Fan, Fleming, and Warren [2013] showed that private asset managers have significant discretion in marking to market their portfolios. Second, the value of private investments may not be easy to calculate. Third, revised values to private equity and venture capital generally are triggered by the addition of new investor capital to the portfolio company—and remain at cost until the next round of financing. Finally, Edelstein and Quan [2006] and Geltner, MacGregor, and Schwann [2003] showed that real estate values are typically based on appraisal values that, in turn, are based on historical, not current, values.

All of these factors can lead to nonsynchronous price changes between the value of private asset portfolios and the value of public securities markets. This means that private asset values may lag behind the public markets, and it can take several calendar periods for all of the systematic risk of the public markets to wash through the private asset portfolio. Not only does this have implications for alpha and beta separation, Marcato and Key [2007] showed how this can have an impact on portfolio construction.

## A DEMONSTRATION OF ILLIQUIDITY

Following through on Burton Malkiel’s dissertation, we track the serial correlation associated with illiquid asset classes. A corollary of Malkiel’s thesis is that no serial correlation is associated with asset classes. The reasoning follows from his main random walk thesis: The prior return associated with an asset class cannot be used to influence or predict the current return to that asset class. However, a demonstration of serial correlation refutes a random walk thesis; it shows that yesterday’s return to an asset value is, in fact, linked to the current return to the asset value.

To test the efficient market thesis with respect to illiquid assets, we track the serial correlation for several periods associated with the returns to private equity, venture capital, and real estate. Private equity, venture capital, and real estate report only quarterly returns, so that is our time period of measure.

Exhibit 1 presents the serial correlation for private equity. It contains two scales. On the left-hand side of the chart is the serial correlation measured with respect to private equity returns. On the right-hand side is the *t*-statistic measuring the statistical significance of the serial correlation. Series 1 (the dashed line) measures the level of serial correlation, and series 2 (the solid line) measures the statistical significance of the serial correlation. We can see that the serial correlation for private equity is statistically significant for three prior periods.^{1} This means that the return to private equity observed in the current period is influenced by the returns to private equity going back three quarters in time.

Exhibits 2 and 3 show similar results for venture capital and real estate. For venture capital, Exhibit 2 shows that the serial correlation is statistically significant going back three periods. In fact, the *t*-statistics are even larger and stronger for venture capital compared to private equity. All of the *t*-statistics are significant at the 1% level or greater.

For real estate, we find statistically significant serial correlation going back four quarters, and all of the *t*-statistics are significant at the 1% level or greater. This is not a surprise; real estate is the most illiquid of asset classes, and it stands to reason that it would have the longest trail of serial correlation associated with its returns. Nonetheless, Exhibit 3 demonstrates that the current returns to real estate are influenced by past returns up to one year in length—a revealing observation. Similar results for hedge fund returns were documented by Lindsey and Weisman [2016].

## USING LAGGED BETAS

The solution for dealing with private assets with nonsynchronous pricing is to use lagged betas to determine the true amount of systematic market risk embedded in their returns. In addition, once the full amount of market risk is taken into accounted, the investor can also determine the true amount of alpha produced by the private asset manager. This method has been documented several times by Anson [2002, 2007, 2013]; Woodward [2011]; and Jian Fan, Fleming, and Warren [2013].

The idea is to expand the traditional capital asset pricing model (CAPM) to include more periods than just the current stock market return. Thus, for example, the returns to venture capital portfolios are regressed against the current public stock market return—consistent with CAPM—as well as the stock market returns from prior periods. These are the *lagged betas*—measuring how much of the stock market return from prior periods affects the current returns to venture capital. How many prior periods must be included in the lagged beta equation depends on the illiquid asset. For example, for real estate returns, Anson [2012] found that the betas associated with the five prior quarters are statistically significant in explaining the amount of systematic market risk embedded in real estate returns.

In this article, we expand the lagged beta analysis to include the four-factor model: market beta, small minus big (SMB; the small cap factor), high minus low (HML; value factor), and momentum.^{2} Although the market beta has been demonstrated to have a significant lagged impact on private asset returns, we wish to determine if these other factors might influence the returns to private assets.^{3}

The purpose of the prior studies was to determine the full amount of market or beta risk embedded in illiquid assets, which previously had not been fully measured. Second, these studies also served to reveal the amount of alpha derived from illiquid assets. Using the lagged beta model, the full amount of systematic market risk and other factors are taken into account, which, in turn, reveals the remaining alpha.^{4}

For this article, we focus on three illiquid asset classes: private equity (leveraged buyouts), venture capital, and real estate. We use data from Cambridge Associates, which, in turn, collects data about private equity and venture capital returns from foundations, pension funds, and endowments that are active investors in these illiquid asset classes. We use the lagged beta technology cited earlier.^{5}

Exhibit 4 contains our results for private equity. In Panel A, we first show the results for a single-period four-factor model to determine the amount of systematic risk associated with private equity. For the single-period model, the beta of private equity is 0.52, with a *t*-statistic of 9.22. We also find in the single-period model that the momentum factor is economically and statistically significant, with a momentum beta of 0.15 and a *t*-statistic of 3.11. The betas for SMB and HML factors are economically small and statistically insignificant. Last, we measure an adjusted R^{2} measure of 0.65 with a statistically significant alpha of 2.3%.^{6}

When we examine Panel B of Exhibit 4, we see that the lagged market betas are statistically significant at the 1% and 5% level going back three prior quarters of market returns. The remaining three factors are statistically insignificant. Importantly, the momentum factor declines significantly to 0.05 with a *t*-statistic of 0.99. Evidently, what appears as momentum in the single-period model is a proxy for the lagged impact of the market betas. Furthermore, the total beta of private equity increases to 0.75 and the R^{2} increases to 0.71. Last, the alpha declines to 1.7%—an indication that a portion of what was previously thought to be alpha associated with private equity returns was nothing more than lagged or delayed systematic market return—good old-fashioned beta.

We find similar results in Exhibit 5 with respect to venture capital. In the one-period model, the beta for venture capital is only 0.53, but we also find a significant (and negative) coefficient for HML and a statistically significant coefficient for momentum. The negative coefficient on the HML value factor indicates that there is a distinct growth bias associated with venture capital—the reciprocal of the value factor, which is not a surprise. Interestingly, we did not find a significant small-cap bias associated with venture capital. In fact, the coefficient on the SMB factor is negative—although statistically insignificant—indicating a bias toward large caps. Last, the alpha is low—only 70 bps—and the R^{2} is 38%.

In Panel B, we see that the market beta remains statistically significant going back four quarters, and the total sum of the market beta is now 0.94. Equally interesting is how far back the HML factor has an impact on venture capital returns—up to three prior quarters. The HML factor remains statistically significant and negative, indicating a persistent growth beta associated with venture capital. The SMB factor remains insignificant, and similar to private equity, the momentum factor fades away when the other lagged factors are included. The R^{2} jumps to 71% in the multiperiod model, and the alpha intercept is basically driven to zero—indicating that, effectively, there is almost no alpha once lagged market factors are taken into account.

It is important to focus for a moment on the impact of the HML factor on venture capital returns. The total lagged beta on this factor (in absolute return) is 0.93, demonstrating a large and significant growth bias. In prior studies, the lagged market beta with venture capital has been found to be in the range of 1.2 to 1.4.^{7} Our results indicate that a portion of this previously documented lagged market beta was, in fact, acting as a proxy for the growth factor.^{8} It is clear that both a significant lagged market beta and growth beta affect venture capital returns; taken together, these two systematic factors account for virtually all of the returns to venture capital because the resulting alpha is driven to zero.

In Exhibit 6, for real estate, we first present the one-period four-factor model. We find a statistically significant market beta, HML, and momentum. The R^{2} is low at 29%, and the alpha is 1.5%.

In Panel B, we present those variables that remain statistically significant when lagged. Not surprisingly, the lagged market beta is significant going back four quarters. We also lag the HML factor to see if it has a lagged impact similar to that it had in venture capital. The results in Panel B show that the HML factor is only relevant for the current quarter’s returns; there is no lagged effect. We also note that momentum, once again, becomes statistically insignificant once the lagged market beta is added. Last, the R^{2} only increases to 47%, and the alpha declines from 1.5% to 100 bps.

In summary, these results confirm the prior empirical studies of lagged market factors and illiquid assets. Lagged factors are an effective method by which an accurate amount of systematic risk can be identified and captured with respect to illiquid assets. For private equity, the lagged market beta is the only factor that remains relevant, whereas for venture capital, we find significant lagged betas for both the market beta and the HML factor. With respect to real estate, lagged market beta remains the key driver of investment returns, but there is also a contemporaneous value impact because the HML factor has a significant impact in explaining the returns to private real estate. Last, it is clear from these results that a component of headline alpha is really nothing more than lagged systematic factors.

## THE LIQUIDITY PREMIUM

Prior papers were primarily concerned with measuring the beta and alpha associated with illiquid asset classes—an important attribute when assessing asset manager performance. A remaining question to address is how much of the return to illiquid assets is due to a liquidity premium. Even after we identify the full amount of systematic risk associated with an illiquid asset class, we still must determine whether the residual alpha contains a component of a liquidity premium.

Unfortunately, liquidity premiums are generally unobservable. Therefore, we have to construct our own liquidity premium. To do this, we turn to a subasset class known as business development companies (BDCs). BDCs are a form of closed-end mutual fund. No redemptions are associated with BDCs; instead, investors in BDCs buy equity shares that are publicly traded.

The protection from redemptions makes BDCs ideal funds in which to invest in illiquid assets. In particular, we examine BDCs that invest in the privately issued debt of below-investment-grade companies. Typically, this debt is subordinated, or it is mezzanine debt issued by credit-risky companies, often as part of a private equity or leveraged buyout deal.

Mezzanine debt is a good instrument from which to derive the liquidity premium because it is a basket of risks:

• Duration risk: It is a bond.

• Credit spreads: Mezzanine debt typically has the same credit risk profile as junk debt.

• A liquidity premium: Mezzanine debt is subordinated debt and trades infrequently and then only at a large discount.

We can observe the first two components of risk associated with mezzanine debt: duration and credit spreads. In addition, we can observe the total return to mezzanine debt. With these pieces, we can back out the liquidity premium. Exhibit 7 demonstrates the liquidity premium puzzle.

To start, we build a basket of BDCs that invest only in mezzanine debt and from which we can calculate a dividend yield. We identify 13 BDCs that fit this description; they are listed in the Appendix. Next, we determine the average debt maturity and duration of this debt basket and match it with a similar-duration U.S. Treasury debt instrument. Last, we calculate appropriate option-adjusted credit spreads to apply to match the credit riskiness of the underlying mezzanine debt. The remainder—which we have to tease out from the data—is our liquidity premium; it is unobservable, but it can be estimated from Exhibit 7.

Exhibit 8 graphs the liquidity premium. A couple of observations are apparent. First, the liquidity premium was very low prior to the Great Recession, only in the range of 1% to 2%. This is consistent with the overwhelming supply of liquidity and credit that flooded the market prior to 2008 and caused the Great Recession. In addition, we note that those private capital funds with vintage years 2006–2008 have done particularly poorly. There simply was too much credit and liquidity prior to the Great Recession, and this caused depressed liquidity premiums and private capital returns.

Not surprisingly, after the Great Recession, liquidity premiums spiked up to 8% and since have come down as massive amounts of quantitative easing have provided stability to the financial markets. Still, once stabilized, the liquidity premium appears to be in the range of about 4% to 5%, which is consistent with the rule-of-thumb return premium over public market returns that is often cited when investing in private assets.

Before continuing, it is important to address several issues regarding the use of BDCs to measure a liquidity premium. First, there is the issue of whether a liquid asset—a BDC—can capture a liquidity premium in its returns. To counter this issue, we do not measure the total (market) return to the equity shares of BDCs because doing so would incorporate stock market risk into our analysis. Instead, we focus on the cash yield that accrues to investors, which is derived from the underlying assets of the BDC and not its share price.

Nonetheless, BDC shares are traded in equity markets; therefore, they contain an equity risk premium. As a result, what we claim to be an illiquidity premium could be, at least partly, the equity risk premium. In fact, in addition to the equity risk premium, the other factors in the Fama–French–Carhart model might account for the liquidity premium.

To address this issue, we present Exhibit 9, in which we regress the returns of the liquidity premium on the four-factor model. Exhibit 9 demonstrates that none of the factors (market beta, SMB, HML, and momentum) is economically or statistically significant with respect to the liquidity premium. In addition, the R^{2} is low at 10%, and the F-statistic for the full regression is not statistically significant. These results demonstrate that the liquidity premium is a separate factor distinct from market beta, SMB, HML, and momentum. Last, the intercept in Exhibit 9, equal to 3.7%, represents the long-term expected return to the liquidity premium.

We also consider the liquidity premium documented here, with other research regarding measuring this premium. One method to measure the liquidity premium is the structure model of Merton [1974]. The Merton credit spread model uses option pricing models to measure the fair value spread on a corporate bond, taking into account the spread for its credit risk and expected losses. The residual spread (liquidity premium) is observable if the Merton model fair-credit-spread estimation does not match the market spread. The difference is attributable to the liquidity premium. This model has documented liquidity premiums of −50 bps to 2.5%.^{9}

Another model compares the yields on risk-free liquid bonds with an equivalent position in corporate bonds protected against default risk using credit default swaps (CDSs). The liquidity premium is then determined to be the Corporate bond spread–CDS premium. Longstaff, Mithal, and Neis [2005] documented this approach, with liquidity premiums observed between 0% and 3.5%.

A third method examines the relative valuation of a pair of financial instruments, which—other than liquidity—are assumed to offer equivalent cash flows, and then compares prices, expected returns, or yields to back out the liquidity premium for the relatively illiquid asset compared to the more liquid asset. One analysis compared covered bonds (bonds backed by the credit quality of large banks as well as an underlying pool of high-grade assets) to interest rate swaps of similar maturity. This method documents liquidity premiums of 0% to 1.5% (Hibbert et al. [2009]).

These prior studies all find a liquidity premium, but the size of the premium is less than that documented in this study. One reason for this difference is that the prior studies all reviewed the liquidity premium associated with publicly traded assets: bonds, CDS, and interest rate swaps. We would expect a larger premium to be associated with illiquid assets.

As a final note, the liquidity premium is also subject to serial correlation. Exhibit 10 demonstrates that the serial correlation for the liquidity premium is statistically significant (at the 10% level) out to three lagged periods.

## LAGGED BETAS AND LIQUIDITY PREMIUMS

We now put all of this together. We include the liquidity premium in our regression equations to determine if this factor provides additional explanatory power with respect to the returns to private asset classes. Our hypothesis is that there is a positive relationship between liquidity premiums and the returns to private asset classes.

In Exhibit 11, we present our final results for private equity, venture capital, and real estate. We find that the liquidity premium is both an economically and statistically significant variable in the pricing of illiquid assets but only on a contemporaneous basis—there is no lagged effect associated with it. For example, for private equity, we observe a factor loading of 0.70 for the liquidity premium. In addition, the R^{2} increases to 0.84 compared to 0.71 in Exhibit 4. We also note that the total lagged market beta remains statistically significant for three lagged periods.

We find similar results for venture capital and real estate: The liquidity premium has a significant and positive impact in explaining the returns to these illiquid asset classes. For venture capital, the liquidity premium has a coefficient almost identical to that of private equity—a value of 0.71. In addition, the R^{2} improves to 0.80 from 0.71 in Exhibit 5. Last, we note that the impact of HML is diminished when the liquidity premium is included: Only the contemporaneous period and one lagged period of HML remain relevant. Interestingly, we now find the small-cap factor to have an impact but only on a contemporaneous basis.

For real estate, we find the largest impact of the liquidity premium with a factor loading of 1.03. In addition, the R^{2} increases from 0.43 to 0.70. Furthermore, only the market beta has any impact in addition to the liquidity premium.

As a last observation, we noted in Exhibit 10 that significant serial correlation is associated with the liquidity premium. Consequently, we expected to observe a lagged impact of the liquidity premium on private asset classes, and we included lagged values of this variable in the results presented in Exhibit 11. Yet, we only observe a contemporaneous impact of the liquidity premium. However, it is interesting to note that in each case (private equity, venture capital, and real estate), there is a subsequent reversal of the impact of the liquidity premium for lagged periods (−1) and (−2). However, these coefficients are not statistically significant; therefore, we cannot draw firm conclusions.

## CONCLUSION

Private equity, venture capital, and real estate are well known to be illiquid asset classes. This lack of liquidity has two important implications for performance measurement. First, the illiquid nature of private assets makes it more difficult to measure the true amount of systematic market factors embedded in their return stream. Not only is the amount of beta hidden by their illiquid nature, the amount of alpha is exaggerated. Using lagged betas reveals the true amount of systematic risk embedded within illiquid asset classes and accurately assesses the amount of alpha produced by these private asset classes. In fact, with respect to venture capital, once the market beta and growth beta are fully taken into account, the resulting alpha is driven to zero.

Second, after accounting for the lagged market risk factors, we discovered that there is still explanatory power associated with the liquidity premium. We did not find the same lagged impact with the liquidity premium as we did with equity market returns, but it is clear that liquidity plays a key role in the returns to private asset classes.

Third, much of the performance measurement of the private capital industry is driven by Public Market Equivalents (PMEs; Kaplan and Schoar [2005]). PMEs are a constructive way to make comparisons between public market returns and the private capital market. However, PMEs do not take into account the lagged betas or the liquidity premium identified in this article and therefore have the potential to overstate the value creation of private equity, venture capital, and real estate.

Last, although we examined only private asset classes, the liquidity premium might also have explanatory power for public, yet less liquid, asset classes. These might include small-cap stocks, high-yield debt, and thinly traded real estate investment trusts. Although we did not explore these asset classes in our study, this remains another avenue for research.

## APPENDIX

## ENDNOTES

↵

^{1}A*t*-stat of 1.72 (for three prior quarters of private equity returns) is statistically significant at the 9% level, whereas the*t*-stats associated with one-period and two-period serial correlation are statistically significant at the 0.01% and 2% level, respectively.↵

^{2}The four-factor model is based on the research of Fama and French [1993] and Carhart [1997].↵

^{3}We are aware that Fama and French [2015] recently introduced two new factors, profitability and investment. However, we decided to use the better-known and well-documented four-factor model cited in the text.↵

^{4}Not only did Anson [2002, 2007, 2013] find statistically significant lagged beta, he also documented a distinct and consistent behavioral aspect to the pricing of illiquid asset returns.↵

^{5}The basic model for measuring lagged betas is presented by Anson [2002, 2007, 2013].↵

^{6}We use quarterly data, so a 2.3% alpha per quarter is approximately 9.2% per year—not a bad excess return.↵

^{7}See Anson [2002, 2007, 2013].↵

^{8}This is a neat point that was conveyed to us by an anonymous referee.↵

^{9}See the excellent summary by Hibbert et al. [2009].

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